First check the gear oil. Dirty/water contaminated oil can be a cause of poor shifting in Hydroelectric lower units. The pump screen gets plugged then it won't port oil to shift.
You can disconnect the electric shift wires at the Stbd side of the powerhead and check voltage coming from the remote control shift switch in Neutral and Reverse. Only the green wire will have 12V to ground in Neutral; both green and blue wires are energized for Reverse.
You can energize both the green (neutral solenoid) and blue (reverse solenoid) wires going to the lower unit, with a 12VDC source. Connect the Negative lead of the power source to a good ground on the block. Positive to the (2) wires. You should get Reverse if things are working properly.
Note that you need at least cranking speed to get enough oil pressure out of the L/U's internal pump, to get a Hydro L/U to shift to Neutral or Reverse. Better to have it running for the check.
Here's Power vs Gear Position for your Hydro:
0V to green or blue: FWD
12V to Green: Neutral
12V to Green and Blue: REV